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    LCM for 12, 24 and 48

    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    What's the Least Common Multiple (LCM) of 12, 24 and 48?

    Answer

    LCM of 12, 24 and 48 is
    48

    (Forty-eight)

    48 is the smallest positive integer that 12, 24 and 48 all divide without a remainder — every other common multiple of the three is a multiple of it.

    Finding the LCM of 12, 24 and 48 by Prime Factorization

    Split all three numbers into prime factors, then take every prime that shows up in at least one of them, each raised to the highest power it reaches there. Multiplying those highest powers gives the least common multiple:

    All Prime Factors of 12: 2 × 2 × 3 (exponent form: 22 × 3)

    All Prime Factors of 24: 2 × 2 × 2 × 3 (exponent form: 23 × 3)

    All Prime Factors of 48: 2 × 2 × 2 × 2 × 3 (exponent form: 24 × 3)

    Prime factor122448Highest power
    222232424
    33333

    LCM = 24 × 3 = 48

    Checking the LCM of 12, 24 and 48 Two Numbers at a Time

    The least common multiple is associative, so three numbers can be handled as two pairs: first the LCM of the first two, then the LCM of that value and the third. Each pair goes through the two-number formula, which uses the greatest common divisor:

    LCM(a, b) = (a × b) ÷ GCD(a, b)

    LCM(12, 24) = (12 × 24) ÷ 12 = 288 ÷ 12 = 24

    LCM(24, 48) = (24 × 48) ÷ 24 = 1,152 ÷ 24 = 48

    LCM(12, 24, 48) = 48

    The pairs may be taken in any order — 24 and 48 first, then 12 — and the answer is the same 48. That is exactly why the two routes on this page agree.

    Related Calculations

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    What is the LCM of 12, 24 and 48?. The LCM of 12, 24 and 48 is 48 — the smallest number all three divide with no remainder. Step-by-step solution for three numbers.
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    LCM Table

    Number 1Number 2Number 3LCM
    122433264
    122434408
    122435840
    12243672
    122437888
    122438456
    122439312
    122440120
    122441984
    122442168
    1224431,032
    122444264
    122445360
    122446552
    1224471,128
    12244848
    1224491,176
    122450600
    122451408
    122452312
    1224531,272
    122454216
    1224551,320
    122456168
    122457456
    122458696
    1224591,416
    122460120
    1224611,464
    122462744

    About "Least Common Multiple of 3 Numbers" Calculator

    This calculator finds the Least Common Multiple (LCM) of three numbers at once, without doing it in two passes. For example, it can help you find out what's the Least Common Multiple (LCM) of 12, 24 and 48? (The answer is: 48). Enter the first number (e.g. '12'), the second (e.g. '24') and the third (e.g. '48'), then hit the 'Calculate' button.
    The Least Common Multiple of three numbers is the smallest positive integer that all three of them divide without a remainder
    "Least Common Multiple of 3 Numbers" Calculator
    Least Common Multiple of
    ,
    and

    FAQ

    What's the Least Common Multiple (LCM) of 12, 24 and 48?

    LCM of 12, 24 and 48 is 48

    How to find the LCM of 12, 24 and 48 by prime factorization?

    Take every prime that appears in 12, 24 and 48 to the highest power it reaches in any one of them and multiply: 2⁴ × 3 = 48.

    Can you get the LCM of 12, 24 and 48 two numbers at a time?

    Yes, and it is the check this page prints. The LCM of 12 and 24 is 24, and the LCM of 24 and 48 is 48 — the same answer, because the least common multiple is associative and does not depend on the order of the three numbers.

    Is 48 divisible by 12, 24 and 48?

    Yes, and by definition it is the smallest positive integer that is: 48 ÷ 12, 48 ÷ 24 and 48 ÷ 48 all come out whole. Any other common multiple of 12, 24 and 48 is a multiple of 48.

    See Also